1. Field of the Invention
A statistical method for explicitly accounting for the difference in vertical scale between 3-D seismic data and stratigraphic measurements made using logging tools.
2. Discussion of Related Art
As is well known to geophysicists, a sound source, at or near the surface of the earth, is caused periodically to inject an acoustic wavefield into the earth at each of a plurality of regularly-spaced survey stations. The wavefield radiates in all directions to insonify the subsurface earth formations whence it is reflected back to be received by seismic sensors (receivers) located at designated stations at or near the surface of the earth. The seismic sensors convert the mechanical earth motions, due to the reflected wavefield, to electrical signals. The resulting electrical signals are transmitted over a signal-transmission link of any desired type, to instrumentation, usually digital, where the seismic data signals are archivally stored for later analytic processing. The travel-time lapse between the emission of a wavefield by a source and the reception of the resulting sequence of reflected wavefields by a receiver, is a measure of the depths of the respective earth formations from which the wavefield was reflected. Certain attributes of the signals such as signal amplitude level and frequency may be related to the type of rock through which the wavefield propagated or from which the wavefield was reflected.
The seismic survey stations of a 3-D survey are preferably distributed in a regular grid over an area of interest with inter-station spacings on the order of 25 meters. The processed seismic data associated with a plurality of seismic traces from a plurality of receivers distributed over an area under survey may be formatted by well-known analytic methods to create a model of a volume of the earth. The model may be structural, showing the physical attitudes of the respective earth strata of an entire geologic sequence such as depth, dip and strike. Alternately the model may be designed to exhibit variations in the level of a selected seismic attribute, such as seismic impedance. Seismic impedance may be statistically related to variations in the texture of some physical property of subsurface rocks such as porosity or lithology. The purpose of such earth models is to select optimal locations for boreholes drilled to recover some desired natural resource such as fluid hydrocarbon products.
A detailed picture of the stratigraphy of the vertical geologic column at a wellsite can be provided by one or more logging tools of any one of many different known types, that may be lowered into a borehole on a wireline, on the drill stem in MWD operations or on coiled tubing. The vertical measurement resolution of wireline tools is very good; it may be on the order of centimeters or often, even millimeters. Horizontally, boreholes are far apart, particularly in newly-developed prospects; the well spacing may be hundreds or more meters. For that reason, the horizontal resolution of log data measurements is very poor.
In a 3-dimensional areal seismic survey, the seismic stations are closely-spaced horizontally, perhaps on the order of 25 meters or less, thus providing excellent lateral resolution. But the vertical, time-scale resolution of seismic data is a function of the frequency of the reflected seismic energy and the wavefield propagation velocity. The vertical resolution of typical low-frequency reflected seismic signals, after processing, may be on the order of tens of meters.
It is useful to statistically relate the laterally sparsely-sampled but vertically detailed borehole measurements of selected rock characteristics with seismic observations which are densely spaced horizontally but poorly resolved vertically. In view of the limited vertical resolution of seismic measurements, seismic attributes are typically correlated with petrophysical well data averaged vertically across earth strata which may be several tens of meters thick. The seismic attributes are then used to guide the areal interpolation of the well-derived zone average data. The techniques of kriging and cokriging are commonly-used geostatistical methods for performing this interpolation task. Kriging is a spatial prediction method for generating the best linear unbiased estimate of a rock property value by statistical interpolation of well data. Cokriging is a spatial prediction method using seismic attributes as secondary data to guide the interpolation of the average rock characteristic measured in wells. Both methods are analogous to Wiener filtering techniques applied in the time domain.
The cokriging method is useful to derive an areal model of an average rock property for a given earth stratum by combining well and seismic data. However, this and other similar techniques do not provide a vertically detailed 3-D model of the subsurface layer. There is a need for constructing such detailed 3-D models from seismic and well log data. Three-dimensional modeling requires careful integration of log and seismic data at different scales. A review of prior integration efforts follows.
S. B. Gorell, in a paper entitled Creating 3-D reservoir models using areal geostatistical techniques combined with vertical well data, 1995, SPE paper 29670, presented at the Western Regional Meeting at Bakersfield, Calif., and C. S. Burns et al. in a paper entitled Reservoir characterization by seismically constrained stochastic simulation, 1993, SPE paper 25656, 8th annual Middle East Oil show, Bahrain, propose an empirical scaling method. Here, each vertical column of cells in a 3-D porosity model is linearly re-scaled to reproduce a seismic derived average porosity map. The technique has the advantage of being straightforward to implement but the re-scaled 3-D model will not tie at deviated wells. Furthermore, the resealing process may distort the data histogram.
C. V. Deutsch et al, in Geostatistical reservoir modeling accounting for precision and scale of seismic data, 1996, SPE paper 36497, Annual Technology Conference, Denver. Colo., introduced an heuristic procedure based on simulated annealing. An objective function was constructed including a term that measures the degree of misfit between vertical average data and average values computed from the 3-D model. Simulated annealing is used to perturb the 3-D model until the misfit is reduced to a value below a specified tolerance. The method has the advantage that is it possible to account for the precision of the average information. The method is, however, very greedy of computer time and suffers from convergence problems when conflicting constraints are present in the objective function.
R. A. Behrens et al. in 1996, also at Denver, in SPE paper 36499 entitled Incorporating seismic attribute maps in 3-D reservoir models, teach a sequential simulation technique based on conventional block kriging. A porosity estimate is obtained for each cell of a 3-D model as a weighted linear combination of adjacent cell porosity data and the seismic derived porosity average of the vertical column containing the cell. The method accounts explicitly for the difference of support volumes between well and seismic data but not for the fact that the seismic porosity averages may not be exact measurements. Compared to simulated annealing, this method has the advantage of being more robust and amenable to analytical analysis. But it involves solving relatively complex kriging systems constructed from average covariance functions.
There is a need for a 3-D simulation method that will account for the difference in scale between seismic and logging data and which will be economical of computer processing time. This disclosure teaches a stochastic interpolation method which may be used to generate a vertically detailed 3-D earth model of a rock characteristic by combining finely-sampled log data with seismic attributes representing vertical average of the rock property of interest.